Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Textbook Question
Chapter 3, Problem 3.116P
Derive the transient, two-dimensional finite-difference equation for the temperature at nodal point 0 located on the boundary between two different materials.
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Students have asked these similar questions
(a) Consider nodal configuration shown below. (a) Derive the finite-difference
equations under steady-state conditions if the boundary is insulated. (b) Find the value of
Tm,n if you know that Tm, n+1= 12 °C, Tm, n-1 = 8 °C, Tm-1, n = 10 °C, Ax = Ay = 10 mm, and k =
W
3
m. k
Ay
m-1, n
11-
m2, 11
m, n+1
m, n-1
The side insulated
(a) Consider nodal configuration shown below. (a) Derive the finite-difference
equations under steady-state conditions if the boundary is insulated. (b) Find the value of
Tm,n if you know that Tm, n+1= 12 °C, Tm, n-1 = 8 °C, Tm-1, n = 10 °C, Ax = Ay = 10 mm, and k
=
=
W
3
m. k
.
Ay
m-1, n
m, n
| Δx="
m, n+1
m, n-1
The side insulated
Q1
Passage of an electric current through a long conducting
rod of radius r; and thermal conductivity k, results in
uniform volumetric heating at a rate of ġ. The conduct-
ing rod is wrapped in an electrically nonconducting
cladding material of outer radius r, and thermal conduc-
tivity k, and convection cooling is provided by an
adjoining fluid.
Conducting
rod, ġ, k,
11
To
Čladding, ke
For steady-state conditions, write appropriate forms of
the heat equations for the rod and cladding. Express ap-
propriate boundary conditions for the solution of these
equations.
Chapter 3 Solutions
Introduction to Heat Transfer
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